Geometrical Equivalence Principle Based Modeling and Analysis for Monolayer Halbach Array Spherical Motor With Cubic Permanent Magnets

This paper proposes a monolayer Halbach array based permanent magnet spherical motor (PMSpM) using cubic permanent magnets (PM). The research aims to provide a fast computing model to calculate the magnetic field for this PMSpM, which helps for future PMSpM optimization and control study. Three thickness equivalence principles are provided and compared for cubic PMs. The magnetic scalar potential is introduced, and the spherical harmonics expansion is implemented for rotor magnetic field analysis. Engineering revision is used to reduce the Legendre function deviation in polar angle direction. Torques and forces are deduced using the Lorentz force law, and relatively simple models of this PMSpM for both magnetic fields and torques are acquired. In addition, a prototype motor has been developed, and the analytic results of air-gap flux density and torque are compared with their finite element simulation and experimental results, which are proved consistent. It is concluded that the fundamental component of the spherical harmonics can be used to present the magnetic field model, which uses fewer integrals than the Biot-Savart law based solution, and the modeling results of the magnetic field flux density, forces and torques are in line with the expectations. The analytic models are proved correct.